Application of Variational Methods to Intermediate and High-Energy Scattering

The application of Schwinger's variational principle to scattering by a Yukawa potential is studied. A detailed comparison of the Born approximation, variational, and exact results is given in the energy region from 20 to 150 Mev for a potential strength and range appropriate to the ${}_{}{}^3{}_{}{}^{}S$ neutron-proton interaction. Comparison with the second Born approximation is also made. The utility of the variational principle is discussed and consideration is given to the high-energy limit. It is judged that for most potentials, the variational formulation without elaborate trial functions will be better than the Born approximation.